The J. C. Penney Company, one of the country's largest department store chains, said yesterday that it would cut its quarterly dividend to 12.5 cents a share from 28.75 cents and invest the extra money in its department stores and Eckerd drugstores. Penney cited ''industry conditions'' for the move and said the new rate will be in line with the dividend rates of its competitors. The company's shares fell 44 cents, or 3 percent, to $14.13 on the New York Stock Exchange after the news. The dividend cut is Penney's second in less than a year. In December, the company, based in Plano, Tex., reduced its quarterly dividend to 28.75 cents a share from 54.5 cents, also to spend more on operations.